Finite-time control of linear systems subject to parametric uncertainties and disturbances
type: Item
instance of: scholarly article
title: Finite-time control of linear systems subject to parametric uncertainties and disturbances
zbMATH Open document ID: 0983.93060
DOI: 10.1016/S0005-1098(01)00087-5
author: F. Amato
author: M. Ariola
author: Peter Dorato
published in: Automatica
publication date: 2002-04-10T00:00:00Z
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 1661408
zbMATH Keywords: uncertain linear systems
zbMATH Keywords: parametric uncertainties
zbMATH Keywords: state feedback finite-time stability
zbMATH Keywords: finite-time boundedness
zbMATH Keywords: disturbance-rejection
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
cites work: Robust and quadratic stability via polytopic set covering
cites work: Q4847220
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: Q4284214
cites work: Stability robustness of interval matrices via Lyapunov quadratic forms
cites work: On a Convex Parameter Space Method for Linear Control Design of Uncertain Systems
cites work: Estimating Reachable Sets
cites work: Q5555195
full work available at URL: s0005-1098(01)00087-5
OpenAlex ID: W1821866767
review text: The authors consider a linear system subject to time-varying parametric uncertainties and to exogenous constant disturbances NEWLINE\[NEWLINE\dot x(t) = A(p)x(t) + B(p)u(t) + G(p)w,NEWLINE\]NEWLINE where \(A(p)\in\mathbb R^{n\times n}\), \(B(p)\in\mathbb R^{n\times m}\) and \(G(p)\in\mathbb R^{n\times l}\). The concept of finite-time boundedness for the state of a system, when not only given initial conditions but also external constant disturbances are considered, is introduced. The main result provided is a sufficient condition guaranteeing finite-time boundedness via state feedback. It can be applied to problems with both non-zero initial conditions and unknown constant disturbances. This condition is turned into an optimization problem involving LMIs. A detailed example is presented to illustrate the proposed methodology.
description: scientific article; zbMATH DE number 1661408